Question

Four students were asked to label angles in pairs of triangles. Their drawings are shown below. Tatyanna Triangle A B C. Angle B is 54.3 degrees and angle C is 61.2 degrees. Triangle X Y Z. Angle Z is 64.5 degrees and angle Y is 54.3 degrees.[Not drawn to scale] Simon Triangle A B C. Angle A is 63.2 degrees and angle B is 58.4 degrees. Triangle X Y Z. Angle Z is 63.2 degrees and angle Y is 58.4 degrees.[Not drawn to scale] Anders Triangle A B C. Angle A is 59.8 degrees and angle B is 60.6 degrees. Triangle X Y Z. Angle X is 59.8 degrees and angle Z is 60.6 degrees.[Not drawn to scale] Kai Triangle A B C. Angle B is 60.9 degrees and angle C is 57.7 degrees. Triangle X Y Z. Angle X is 61.4 degrees and angle Z is 57.7 degrees. [Not drawn to scale] Which student labeled the triangles such that Triangle A B C is similar to X Y Z? Tatyanna Simon Anders Kai

Answer 1

Answer: I’m confident with Kai being the correct answer

Answer 2

Kai labeled the triangles such that ΔABC is similar to ΔXYZ.

What is a triangle?

A triangle is a two-dimensional geometrical figure that has three sides, three vertices, and three interior angles.

As per Tatyanna:

In ΔABC, ∠B = 54.3°, ∠C = 61.2°

Therefore, ∠A = 180° - (54.3° + 61.2°) = 64.5°

In ΔXYZ, ∠Z = 64.5°, ∠Y = 54.3°

Therefore, ∠X = 180° - (64.5° + 54.3°) = 61.2°

As per Simon:

In ΔABC, ∠A = 63.2°, ∠B = 58.4°

Therefore, ∠C = 180° - (63.2° + 58.4°) = 58.4°

In ΔXYZ, ∠Z = 63.2°, ∠Y = 58.4°

Therefore, ∠X = 180° - (63.2° + 58.4°) = 58.4°

As per Anders:

In ΔABC, ∠A = 59.8°, ∠B = 60.6°

Therefore, ∠C = 180° - (59.8° + 60.6°) = 59.6°

In ΔXYZ, ∠X = 59.8°, ∠Z = 60.6°

Therefore, ∠Y = 180° - (59.8° + 60.6°) = 59.6°

As per Kai:

In ΔABC, ∠B = 60.9°, ∠C = 57.7°

Therefore, ∠A = 180° - (60.9° + 57.7°) = 61.4°

In ΔXYZ, ∠X = 61.4°, ∠Z = 57.7°

Therefore, ∠Y = 180° - (61.4° + 57.7°) = 60.9°

Therefore, the sequence and the value of the angles for ΔABC and ΔXYZ matches only with Kai's drawings.

Therefore, as per his drawings, ΔABC and ΔXYZ will look similar.

Learn more about a triangle here: https://brainly.com/question/22483552

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